Short-pulse laser device with a preferably passive mode coupling and multiple reflection telescope therefor

ABSTRACT

The invention relates to a short-pulse laser device ( 11 ) with a preferably passive mode coupling. Said device comprises a resonator ( 12 ) which contains a laser crystal ( 14 ) in addition to several mirrors (M 1 -M 7 , OC) that define a long resonator arm ( 17 ) and a short resonator arm ( 16 ), one (M 1 ) of said mirrors forming a pump beam coupling-in mirror and another (OC) forming a laser beam output coupler and comprising a multiple reflection telescope ( 18 ) that increases the length of the resonator and is allocated to the resonator arms ( 16, 17 ). Said telescope is constructed using mirrors ( 25, 26 ), in order to reflect a laser beam ( 15 ) that is coupled into the space between them back and forth several times, prior to being decoupled back into the other resonator, whereby sequential eccentric reflection points ( 1  to  8; 1 ′ to  8 ′) on the mirrors ( 25,26 ) are offset in relation to one another. The telescope ( 18 ) comprises only one curved mirror ( 26 ), in addition to a planar mirror ( 25 ), whose position corresponds at least substantially to the centre ( 25 ′) of an imaginary multiple reflection assembly comprising two curved mirrors ( 26   a,    26   b ), whereby the one curved mirror ( 26 ) of the telescope ( 18 ) also contains the reflection points of the other imaginary curved mirror. The invention also relates to a multiple reflection telescope ( 18 ) for said device.

The invention relates to a short pulse laser device with preferablypassive mode-locking, with a resonator containing a laser crystal aswell as several mirrors which define a long resonator arm as well as ashort resonator arm, one of which forms a pump beam in-coupling mirror,and another one forms a laser beam out-coupler, and with a multiplereflection telescope increasing the resonator length and associated toone of the resonator arms, which telescope is constructed using mirrorsin order to reflect a laser beam that is coupled into the space betweenthem back and forth between the mirrors several times before it isout-coupled back into the remaining resonator, sequential eccentricreflection points on the mirrors being offset relative to one another.

Likewise, the invention relates to a multiple reflection telescope for ashort-pulse laser device for increasing its resonator length, whichmultiple reflection telescope is constructed using mirrors so as toreflect a laser beam coupled into the space between them back and forthbetween the mirrors several times before it is out-coupled back into theremaining laser device, sequential eccentric reflection points on themirrors being offset relative to one another.

Recently, short-pulse laser devices have become increasinglyinteresting, since with a view to the extremely short pulse durations inthe femtosecond range, with peak pulse outputs of >1 MW, the mostvarying applications in science and industry become possible. Thus, suchshort-pulse laser devices having pulse durations in the femtosecondrange can be used for the time-resolved investigation of the interactionbetween electromagnetic radiation and matter. On the other hand, with aview to the increasing miniaturization in material processing, it hasbecome possible to produce the finest structures with precision and highspeed. Femtosecond laser devices with a high output pulse energy and ahigh repetition rate are ideal to be employed for this. What isdesirable in this respect is a laser device which produces laser pulseshaving a pulse duration in the order of 10 fs as well as an energy of,for example, 25 to 30 nJ at a pulse repetition rate in the order of 10MHz. The pulse repetition rate which, compared to earlier laser devices,is relatively slow in the femtosecond range (in the order of 10 MHzinstead of 80 MHz, e.g.) in a common titanium-sapphire-fs laser isdesired because then a higher pulse peak output, put, or a higher pulseenergy, respectively, can be achieved, which is of interest for theprocessing of material. However, such comparatively low repetition rateswhich,. vice versa, mean a relatively long pulse round trip time in thelaser resonator, by mere calculation yield a corresponding increase inthe length of the resonator, e.g. from 2 m to 16 m, causing an increasein the dimensions of the laser device.

Based on an earlier publication by D. Herriott et al., “Off-Axis Pathsin Spherical Mirror Interferometers”, Applied Optics, April 1964, vol.3, No. 4, pp. 523-526, lenghtening of the pulse round trip times hasthen been suggested by S. H. Cho et al. in the article “Generation of90-nJ pulses with a 4-MHz repetition-rate Kerr-lens mode-locked Ti:Al₂O₃laser operating with net positive and negative intracavity dispersion”,Optics Letters, 15 Apr. 2001, vol. 26, No. 8, pp.560-562, by providing amultiple-pass resonator part, here also called “multiple reflectiontelescope” or “tele-scope” in short (according to the article by A.Poppe et al., “A Sub-10 fs, 2.5-MW Ti:Sapphire Oscillator”, UltrafastOptics 1999, pp. 154-157, Ascona, Switzerland (1999)), to thus increasethe duration of the pulse round trip by a multiple passage in thisresonator part, due to a plurality of reflections on mirrors arrangedopposite each other, and to thereby lower the repetition rate. In thismanner it becomes possible to increase the energy portion of the pulsepart that is out-coupled per round trip.

However, what is detrimental with these known laser devices, ortelescopes, respectively, is that relatively large dimensions are stillrequired for the laser resonator so that the dimensions of the laserdevice in sum result in a relatively bulky device. Furthermore, in theknown laser devices also the stability of the laser radiation poses aproblem, and it must be taken into consideration that the telescope willcause images of the laser beam cross-section which, for stabilitypurposes, must be adapted as good as possible to the remainingresonator. However, in the known devices, the situation is such thatalready slight imprecisions in the positions of the mirrors of thetelescope and thus already relatively slight resonator length changesresult in substantial changes in the beam cross-section, with theconsequence of overall instabilities in the resonator. Furthermore, itis detrimental that in the laser device known from the article by Cho etal., where the laser beam is coupled into the telescope part by slits inone of the telescope mirrors and is out-coupled again from thistelescope part by corresponding slits in the mirror, the mirror designis complex, and the production thereof poses problems.

Therefore, it is an object of the invention to allow for an increase inthe peak pulse output in a short-pulse laser device as initiallydefined, by increasing the pulse round trip time in the laser devicewith nevertheless comparatively small resonator dimensions; furthermore,a good adaptation of the telescope to the remaining resonator and, thus,a high stability in the laser beam production shall be renderedpossible, and also an exact fine adjustment of the adaptation to theresonator parts shall be feasible. Furthermore, it is an object of theinvention to provide simple adapted means for the in- and out-couplingof the laser beam in the region of the telescope of the resonator.

The inventive short-pulse laser arrangement of the initially definedtype is characterized in that the telescope has only one curved,preferably concave, mirror as well as a plane mirror whose position atleast substantially corresponds to the middle of an imaginary multiplereflection arrangement with two curved mirrors, whereby the one curvedmirror of the telescope also contains the reflection points of theimaginary other curved mirror.

Likewise, the invention provides a telescope as initially defined andincluding the characteristic features that as telescope mirrors, onlyone curved, preferably concave, mirror as well as a plane mirror areprovided, the position of the plane mirror corresponding at leastsubstantially to the middle of an imaginary multiple reflectionarrangement with two curved mirrors, whereby the one curved mirror ofthe telescope also contains the reflection points of the imaginary othercurved mirror.

Due to the aforementioned design, the teslescope is practically halvedin its dimensions and “folded”. This measure is based on the findingthat when reflected on a curved mirror, the wave front of the laser beamdescribes a likewise curved area, the wave front then changing until itsreflection on an oppositely arranged mirror such that it will correspondto the curvature prevailing there, a situation being achieved in themiddle therebetween in which the wave front is plane; at this site,according to the invention, the plane mirror is arranged. Apart from thereduction in dimensions attained thereby, a substantial advantage isalso seen in the fact that the plane mirror—usually multilayer mirrorsof dielectric materials are used in laser resonators—can be produced atsubstantially more favorable prices than curved substrate mirrors. As anadditional advantage it results with this device that for in-coupling ofthe laser beam, or for its out-coupling, sufficient space is availablewhen this in-coupling and out-coupling occurs approximately in themiddle between the curved mirror and the plane mirror, since there theneighboring beam paths created in the course of the multiple reflectionsare relatively widely spaced apart so that, as will be explained lateron, appropriate in- and out-coupling mirrors can be mounted for“breaking up” the one beam, or beam path, respectively, without anyproblems. By this, on the other hand, the mirrors responsible for themultiple reflections can be produced without any slits, through-bores orthe like.

With a view to the stability of the laser radiation as well as to thedesign of the telescope's mirrors, which is to be as simple as possible,as well as to as low a load as possible on the mirrors during operation,it has further proven advantageous if on the one curved mirror,alternatingly reflection points of this mirror as well as reflectionpoints of the imaginary other curved mirror are arranged on an imaginarycircle line at arc distances corresponding to each other. With thisdevice, thus, there will be no “inter-leaving” of the beam paths of thelaser radiation between the mirrors of the telescope, much rather, thebeam paths which the laser beam follows during the multiple reflections,will be zig-zag-like, corresponding to an approximate cylinder surfaceor frustoconical surface between the mirrors.

With a view to the specially sought increase in the pulse round trip forthe design of the short-pulse laser device for an application inproduction technology, it is furthermore, suitable if a total of eightreflection points is provided on the one curved mirror.

For the stability of the laser radiation, and during the adaptation oftelescope and resonator, respectively, it is advantageous if thedistance between the mirrors and the radius of curvature of the curved,concave mirror correspond to the relation L/R=1±{square root}{overscore((1+cos α)/2)}; wherein

-   -   L is twice the distance between the curved mirror and the plane        mirror,    -   R is the radius of curvature of the curved mirror, and α is the        central angle between two respective consecutive reflection        points actually associated to the one curved mirror and located        on a circle line.

For a simple, stable embodiment, here it is further provided for thecurved mirror of the telescope to be a concave mirror, for which itholds:L/R=1−{square root}{overscore ((1+cos α)/2)}.

As has already been mentioned, with the inventive design with the“folding” of the telescope, a suitable possibility for in- andout-coupling the laser beam in the region of the telescope is provided,and accordingly, a particularly advantageous embodiment of theshort-pulse laser device according to the invention is characterized inthat substantially in the middle between the curved mirror and the planemirror, in- and out-coupling mirrors for the laser beam are provided inthe path of one of the beam paths between these two mirrors.

Finally, for stability purposes, for a better adaptation of thetelescope to the remaining resonator, it is particularly advantageous ifthe telescope is associated with the long resonator arm. Namely,investigations have shown that at the long resonator arm, a laser beamwith a relatively large cross-section is available for in-coupling intothe telescope part, wherein, with the present telescope design, thecross-section of the laser beam changes only slightly during thedifferent reflections in the telescope part, before —practically withthe same cross-section as during in-coupling—it is out-coupled again andsupplied to the remaining resonator part. By this, any possible minorlength changes, i.e. minor changes in the distances between the lensesof the telescope, have hardly any effect since by this the beamcross-section does not change substantially. In this manner, an optimumadaptation between the telescope and the remaining resonator is renderedfeasible.

In the following, the invention will be explained in more detail by wayof preferred exemplary embodiments illustrated in the drawings to which,however, it shall not be restricted. Therein,

FIG. 1 shows a schematic representation of the set-up of a short-pulselaser device with telescope according to the invention;

FIG. 2 shows such a short-pulse laser device when arranged on a mountingplate, also in- and out-coupling of the laser beam in the region of thetelescope being schematically depicted;

FIG. 3 schematically shows a view of a conventional telescope with twoconcave curved telescope mirrors;

FIGS. 4 and 5 show schematic views of this telescope mirrors with thereflection points thereon;

FIG. 6 shows an imaginary intermediate step during a “folding” of such atelescope according to FIG. 3, by providing a plane telescope mirror;

FIG. 7 shows a view of a telescope formed according to the invention,with a concave curved mirror and a plane mirror, also in-coupling of thelaser beam into the telescope as well as out-coupling of the laser beamfrom the telescope being schematically illustrated;

FIG. 8 shows the concave curved telescope mirror of FIG. 7 with thereflection points in a schematic view according to FIGS. 4 and 5;

FIG. 9, in a diagram, shows the course of the radius R (in mm) of thelaser beam in transverse direction versus a distance x (in m) passed bythe laser beam in the resonator, with a short resonator arm, a longresonator arm and the telescope associated therewith;

FIG. 10, in a diagram and by way of four examples, shows the changes inthe beam diameter versus the space between the telescope mirrors so asto illustrate the adaptation of the laser beam with a view to thestability; and

FIGS. 11, 12, 13, 14 and 15, in diagrams similar to FIG. 9, show thecourse of the transversal beam radius R′ versus the distance x passed infive actual devices.

In FIG. 1, a short-pulse laser device 11 is schematically illustrated inwhich, for instance, the Kerr-lens mode locking principle known per seis used for generating the short-pulse laser.

According to FIG. 1, the laser device 1 comprises a resonator 12 towhich a pump beam 13, an argon laser beam, e.g., is supplied. The pumplaser itself, the argon laser, e.g., has been omitted in FIG. 1 for thesake of simplicity and is part of the prior art.

After passing through a lens L1 and a dichroic mirror M1, the pump beam13 excites a laser crystal 14, a titanium:sapphire(Ti:S) solid lasercrystal in the present example. The dichroic mirror M1 is permeable forthe pump beam 13, yet highly reflective for the Ti:S laser beam. Thislaser beam 15, the resonator beam, then impinges on a laser mirror M2and is reflected by the latter to a laser mirror M3. This laser mirrorM3 again reflects the laser beam to a laser mirror M4, and from therethe laser beam 15 is reflected back to the laser mirrors M3, M2 and M1,passing through the laser crystal 14 a second time. This resonator partincluding the mirrors M2, M3 and M4 forms a so-called short resonatorarm 16 which is Z-shaped in the example shown.

From the mirror M1, the laser beam 15 then is reflected to a lasermirror M5 and from the latter to a laser mirror M6 as well as to afurther laser mirror M7, whereby a second Z-folded resonator arm 17 isformed, which is provided as long resonator arm 17. From the lasermirror M7, the laser beam 15 gets into a telescope 18 merelyschematically shown in FIG. 1, and from there it gets to an end mirrorOC acting as an out-coupler. Via this out-coupler end mirror OC, a partof the laser beam 15 is out-coupled under provision of a compensationpossibility, with a compensation platelet CP as well as mirrors notfurther illustrated and made in thin-film technique providing for adispersion compensation as well as for preventing undesired reflectionsin the direction of laser resonator 12 from occurring.

The laser crystal 14 is a plane-parallel body which is opticallynon-linear and forms a Kerr element which has a greater effectiveoptical thickness for higher field strengths of the laser beam 15, yet aslighter effective thickness where the field strength, or intensity,respectively, of the laser beam is lower. This per se known Kerr effectis utilized for self-focusing of the laser beam 15, i.e. the lasercrystal 14 constitutes a focusing lens for the laser beam 15.Mode-locking may furthermore be realized in a per se conventionalmanner, e.g. by means of an aperture not further illustrated in FIGS. 1and 2 (cf. e.g. AT 405 992 B); however, it would also be conceivable todesign an end mirror, e.g. M4, as a saturable Bragg reflector and thususe it for mode-locking.

The mirrors M1, M2 . . . M7 are made in thin-film technique, i.e. theyare comprised of many layers which, when reflecting the ultra-shortlaser pulse—which has a large spectral bandwidth—, fulfill theirfunction. The different wave length components of the laser beam 15enter to different depths into the layers of the respective mirrorbefore being reflected. In this manner, the different wave lengthcomponents are delayed at the respective mirror for different amounts oftime; the short-wave components will be reflected rather outwardly (i.e.towards the surface), the long-wave components, however, will bereflected deeper within the mirror. By this, the long-wave componentswill be temporally delayed relative to the short-wave components. Inthis manner, a dispersion compensation can be attained insofar as pulsesof a particularly short time range (preferably in the range of 10femtoseconds and therebelow) have a wide frequency spectrum; this is aresult of the fact that the different frequency components of the laserbeam 15 in the laser crystal 14 “see” a different refraction index(i.e., the optical thickness of the laser crystal 14 is differentlylarge for the different frequency components, and the differentfrequency components therefore will be differently delayed when passingthrough the laser crystal 14. This effect can be counteracted by theabove-mentioned dispersion compensation at the thin film laser mirrorsM1, M2 . . . M7.

What has so far been described is a per se conventional set-up of ashort-pulse laser with mode-locking, and a detailed description of thelatter therefore is not required.

In operation, with each round trip of the laser beam 15 in the shortresonator arm 16 as well as in the long resonator arm 17, a part of thelaser pulse is out-coupled by means of the out-coupler OC as mentionedbefore. In practice, the length of a laser resonator 12 withouttelescope 18 may be approximately 2 m, a repetition rate according to afrequency of 75 to 100 MHz, e.g. 80 MHz, being achieved, for instance.In order to achieve a higher pulse peak output, i.e. pulse energy, byincreasing the round trip time and, thus, by reducing the repetitionrate, with a view to using the laser device 11 e.g. for the processingof material, the length of the laser resonator 12 is enlarged by theinstallation of the telescope 18. When multiplying the entire resonatorlength by the factor eight, which means for instance with a resonatorlength of approximately 15 m or 16 m, the repetition rate may then liee.g. at approximately 10 MHz. To achieve this long path lengths for thelaser pulses, a mirror arrangement is provided in the telescope 18 so asto achieve a multiple reflection of the laser beam 15 whereby theconstruction length of the telescope 18 can be shortened according tothe multiple reflections.

In FIG. 2, the arrangement of such a laser device 11 according to FIG. 1on a mounting plate 19 is schematically illustrated, which has a size atimes b of for instance a=900 mm times b=450 mm. On this mounting plate19, the part 20 of the laser resonator 12 framed in broken lines in FIG.1 is mounted encapsulated in a housing, and furthermore also the pumplaser 21 is arranged on the mounting plate 19, from which the pump beam13 is supplied to the laser resonator part 20 via two mirrors 22, 23.From this resonator part 20, the laser beam 15 emerges in the directionof laser mirror M6, by which it is reflected to laser mirror M7, as hasbeen described. From there, the laser beam 15 enters the telescope 18,an in-coupling mirror 24 being arranged in the telescope 18, e.g. in ahousing, in one of the several beam paths between two oppositelyarranged telescope mirrors 25, 26. This in-coupling mirror 24 reflectsthe laser beam 15 to the one—in FIG. 2 left-hand—plane telescope mirror25 which then will reflect the laser beam 15 to the oppositely arranged,concavely curved telescope mirror 26. Then the laser beam 15 will bereflected back and forth several times, e.g. eight times, between thesetwo telescope mirrors 25, 26, in this example a total of 8 reflectionpoints corresponding to the eight laser beam reflections being providedon the concavely curved telescope mirror 26 on an imaginary circle lineabout the center of the concave mirror 26, as will be explained in moredetail hereinafter by way of FIG. 8 in connection with FIG. 7.

Finally, the laser beam 15 is coupled out of the telescope 18 by meansof an out-coupling mirror 27 which is arranged in the vicinity of thein-coupling mirror 14 in the same beam path as the former, and whichreflects the laser beam 15 to a further mirror 28 from where the laserbeam 15 gets to the outcoupler OC via mirror 29. To simplify matters,these mirrors 28, 29 are not further illustrated in the schematicillustration of FIG. 1. Besides, if a telescope 18 were not present, theposition of the end mirror (outcoupler) OC would be the position of thelaser mirror M6 in FIG. 1.

An important aspect in a short-pulse laser device with an increasedlaser pulse round trip time is the stability of the laser oscillation,wherein an appropriate adaptation must be effected with a view to imagesof the laser beam cross-section caused by the individual mirrors. Afurther important aspect which is of special importance particularly forindustrial applications, i.e. in the case of the processing ofmaterials, is the compactness of the laser device 11; the aforementioneddimensions of 900 mm×450 mm correspond to conventional laser devices forindustry, wherein, however, here (cf. FIG. 2) additionally the telescopepart 18—which may also form a separate unit—is built in so that thelonger round trip times of the laser beam 15 desired and thus the higherpulse energies can be achieved without an increase in dimensions. Whatis sought is pulse energies in the order of several hundred nJ insteadof the earlier less than 10 nJ. With this, peak pulse outputs of morethan 2 MW can be achieved.

Other than in earlier laser devices with a telescope, in the presentlaser device 11, the telescope 18, as mentioned, is associated with thelong resonator arm 17, since this is advantageous for the stability ofthe oscillation, as will also be explained in more detail hereinafterwith reference to FIG. 9. In the telescope 18, the laser beam 15 movesback and forth several times, e.g. eight times, between the mirrors 25,26 in zig-zag manner approximately along an imaginary cylindricalsurface or frusto-conical surface; when arranging the in-coupling mirror24 and the out-coupling mirror 27 approximately in the middle of thelength of the telescope 18, there will be sufficient space for themirrors 24, 27, since the distance to the next beam path at thislocation is relatively large so that the other beam paths of the laserbeam 15 between the mirrors 25, 26 will not be adversely affected. Whatis important here is also the so-called “weakly focusing” arrangementprevailing here, which will be explained in more detail later on.

For the present embodiment it is particularly important that anextremely short telescope part 18 is attained despite the lengthening ofthe path length of the laser beam 15 to, for instance, the 8-fold by avery special configuration which shall now be explained in more detailby way of FIGS. 3 to 8.

In FIG. 3, a per se conventional basic set-up of a telescope with twoconcavely curved mirrors 26 a, 26 b is illustrated, a laser beam 15being reflected back and forth several times between the two mirrors 26a, 26 b. The type of reflection is such that the laser beam is reflectedback and forth in zig-zag manner in an approximately cylindricalgenerated surface, i.e. between the reflection points 1 to 5 (and,further on, to 8, wherein the reflection points 6, 7 and 8 in FIG. 3 arearranged in congruence to the reflection points 4, 3, and 2, cf. alsothe pertaining FIGS. 4 and 5). Of course, when speaking of azig-zag-like course “according to a cylindrical generated surface”, thisis not quite precise because the individual beam paths between themirrors 26 a, 26 b are straight and extend obliquely so that they cannotform generatrices of the cylinder surface, yet the course of themultiply reflected laser beam 15 can be relatively well approximated ascorresponding to such a cylindrical surface.

The zig-zag-like course, or the angular offset, respectively, of theindividual beam paths also results from the two schematic (inner side)views of the mirrors 26 a, 26 b according to FIGS. 4 and 5, where thereflection points of the laser beam 15 on the mirrors 26 a, 26 b,numbered from 1 to 8, are shown. There, the beam moves from thereflection point 1 on mirror 26 a to the reflection point 2 angularlyoffset relative thereto, on the other mirror 26 b, and from there to the—again angularly offset—reflection point 3 on mirror 26 a and so on. Inthe exemplary embodiment illustrated, there results a central angle α of90° at each mirror 26 a, 26 b, as angular offset for the associatedreflection points, e.g. 2 and 4. In case of more than the 2×4reflections, the central angle α will be accordingly smaller.

The type of multiple reflection between the mirrors 26 a, 26 b of thetelescope 18 previously explained by way of FIGS. 3 to 5 is also termedas “weakly focusing” arrangement. On the other hand, a “highly focusing”arrangement would be given if, e.g., from the reflection point 1 onmirror 26 a the laser beam were reflected to reflection point 6 onmirror 26 b, and from there to point 3 on mirror 26 a, and from thereagain to reflection point 8 on mirror 26 b, to the reflection point 5 onmirror 26 a, to reflection point 2 on mirror 26 b, to reflection point 7on mirror 26 a and to reflection point 4 on mirror 26 b, before the beamis reflected back in the direction to reflection point 1. With this beamcourse, a bundling or “focusing” would be obtained in the region of themiddle 25′ between the two mirrors 26 a, 26 b, schematically shown by abroken line in FIG. 3. Investigations have shown that for the presentdesign of the telescope 18, as already suggested in FIG. 2 and to besubsequently described in more detail with reference to FIGS. 7 and 8,the weakly focusing arrangement resulting from FIGS. 3 to 5 is moresuitable, particularly since the beam paths then are appropriately farapart in the region in question between the middle 25′ and the telescopemirror 26. As will be explained hereinafter, the plane mirror 25 (cf.also FIG. 6) will be arranged in the middle 25′, and since between thismiddle 25′ and the concave mirrors 26 a, and 26 b, respectively, thebeam paths in a weakly focusing arrangement are still sufficientlyspaced apart, it is possible without any problems to accommodate thein-coupling mirror 24 and the out-coupling mirror 27 by breaking upmerely one beam path.

In FIG. 5, also the consecutive numbers of the—appropriatelyoffset—reflection points for the instance of the highly focusingarrangement have been indicated in parentheses beside the numbers 2, 4,6 and 8, for the reflection points for the weakly focusing arrangement,for the purpose of a better illustration.

From FIG. 3 it is furthermore explainable that the laser beam 15 in therespective beam path, e.g. from reflection point 1 to reflection point2, at first has a wave front with a curvature corresponding to thecurvature of the mirror 26 a, which then changes into an oppositecurvature corresponding to that on mirror 26 b in reflection point 2. Inthe middle 25′ therebetween, there is a situation with a plane wavefront. This is utilized by the present invention in that a plane mirror,telescope mirror 25, is arranged in this middle 25′. Then the twotelescope mirrors 26 a, 26 b shown in FIG. 3 are “folded”, i.e. broughtinto congruence, as appears from the schematic illustration in FIG. 6 inan imaginary intermediate step. For the purpose of an improvedunderstanding, it is illustrated that the mirror 26 a is pivoted aboutthe middle 25′ into the other telescope mirror 26 b, until the twomirrors 26 a, 26 b moved into one another have the same position andthus yield the concavely curved telescope mirror 26 according to FIGS. 2and 7. The plane mirror 25 arranged according to the original middleplane 25′ will then be located opposite thereto, cf. FIG. 7.

From this “folding” of the conventional telescope there also results thehalving of the length dimension in the inventive telescope 18 as well asfurthermore that now all the reflection points 1 to 8 according to FIGS.3 to 5 are present on the one remaining concavely curved mirror 26, cf.also FIG. 8 in addition to FIG. 7, in which these reflection points 1 to8 are visible in a schematic illustration of the mirror 26. In addition,in FIG. 8 also the central angle α which is decisive for the angularoffset has been entered. To facilitate distinguishing, the reflectionpoints originally present on a mirror 26 a are illustrated by smallcircles (reflection points 1, 3, 5 and 7), whereas the reflection points2, 4, 6, 8 originally present on the other mirror 26 b have beenillustrated by crosses. In the thus-obtained, final inventivearrangement therefore the reflection points 1 to 8 of the one and of theother telescope mirror 26 a, 25b, respectively, follow each otheralternately, each offset relative to the other by an angle α/2, andopposite thereto, with an offset thereto by an angle according to α/4,there are the reflection points 1′ to 8′ on the plane mirror 25, cf.FIG. 7.

Accordingly, the telescope design according to FIG. 7 can also be viewedsuch that the mirror 26 corresponds to the mirror 26 b of FIG. 3,wherein it additionally contains the reflection points of the otherconcave mirror 26 a. As the counter-piece to this “combined” concavetelescope mirror 26, the plane mirror 25 will then serve whose distance(L/2) from the telescope mirror 26 thus corresponds to half the distance(L) between the telescope mirrors 26 a, 26 b of FIG. 3.

FIG. 9 shows the progress of the transversal radius R′ of the laser beam15 in dependence on the path x thereof through the laser device 1, itbeing visible that there exists a relatively small beam cross-section onthe end mirror M4 of the short resonator arm 16 which then increases inthis short resonator arm 16 as far as to the laser crystal 14; as hasalready been discussed, the laser crystal 14 causes focusing of thelaser beam, which is visible by the narrow indentation in the curve ofFIG. 9. Subsequently, the long resonator arm 17 follows as far as to thesupply of the laser beam to telescope 18, the beam cross-section at theentrance of the telescope 18 being relatively large. This fact is alsoutilized by the present device, since in this manner a good stabilitycan be achieved in the oscillator without any problems, since during themultiple reflections in the telescope 18—cf. also the reflections inFIG. 9 provided with the numbers corresponding to the reflection points1 to 8 in telescope 18 —only slight changes in the beam cross-sectionprevail in each case, other than would be the case if the telescope wereassociated to the short resonator arm 16. By this, a stable oscillationcan be achieved in the laser device 11 without any problems, also slightchanges in length hardly leading to any instability.

The diagram of FIG. 9 is only quite schematic and shall illustrate therelations with the inventive, particularly preferred embodiment of thelaser device 11—with weakly focusing arrangement and association of thetelescope 18 to the long resonator arm 17. On the other hand, FIGS. 11to 14 show computer simulations to quite concrete embodiments, whereinalso the situation for highly focusing arrangements, or for such withtelescopes 18 associated with the short resonator arm 16, respectively,are illustrated. In these diagrams, also the reflection points 1 to 8,the resonator arms 16, 17 as well as the laser crystal 14 are enteredfor greater ease of understanding.

Yet, at first an explanation regarding the stability of the entiresystem shall be given by way of FIG. 10. For this, the relationL/R=1±{square root}{overscore ((1+cos α)/2)} is important, wherein

-   -   L is twice the distance between the curved mirror 26 and the        plane mirror 25,    -   R is the radius of curvature of the curved, concave mirror 26,        and    -   α is the central angle between two respective sequential        reflection points actually associated to the one curved mirror        and located on a circle line.

Departing from the fact that, as previously explained by way of FIGS. 7and 8, a total of eight reflection points 1 to 8 are present (i.e., fourreflection points for each—imaginary—curved mirror 26 a, 26 b), thecentral angle amounts to α=90°, as also appears from FIGS. 4, 5 and 8.Furthermore, the sign “−” in the above-indicated relation corresponds tothe previously explained weak-focusing arrangement (whereas the sign “+”holds for the highly focusing arrangement). Accordingly, for the examplewith a total of eight reflection points 1 to 8 and for the weak-focusingarrangement it results from the aforementioned relation:L/R=1−{square root}{overscore (1/2)}

Hence follows that the relation L/R=0.293. For a mirror radius of R=5000mm (radius values for concavely curved mirrors commonly are indicatedwith a “−” sign, cf. also FIG. 10, yet here they are given without signso as to simplify matters), thus there results a distance between themirrors 26 a, 26 b of L=1465 mm. This distance L would be too large fora discrete set-up (cf. the mounting plate dimension a=900 mm in the caseof the embodiment of FIG. 2), yet with the “folding” of the telescope 18described by way of FIGS. 6 and 7, this distance leads to a highlyadequate arrangement in which the curved mirror 26 and the plane mirror25 are spaced apart precisely by L/2=732.5 mm.

In the instance of a highly focusing arrangement, as in principle isshown in the initially mentioned document by Cho et al., a bundling ofthe beam paths is effected between the two concavely curved mirrors, asmentioned, and in this highly focusing arrangement the sign “+” must beused in the above relation, from which the relation L/R will then yielda value of L/R=1.707. With a distance between the mirrors of L=1465 mm,this will mean for a radius R of the respective telescope mirror ofR=L/1.707=858 mm. With such a concavely curved mirror 26 and a planemirror 25 at a distance of L/2=732.5 mm, the reflection points accordingto the numbers indicated in parentheses in FIG. 5 would be obtained.

In FIG. 10, the x-axis is exactly the (double) mirror-distance L(logarithmically shown). A box has been drawn around the arrangementrealized in practice (cf. also FIG. 12). The associated curved 30 isformed in that the telescope 18 is coupled into the long arm 17 of theoscillator (1200 mm). If the radius R is changed, the distance L willchange. If the relative (i.e. percent) change AD of the beam diameter inthe other arm 16 is calculated, i.e. at the end mirror M4, there resultsa value which has been entered on the y-axis in FIG. 10. The maximum ofthe stability is precisely at that location where the beam diameter doesnot change despite a change of the telescope 18, i.e. at zero. In FIG.10, curves 31, 32 and 33 have also been illustrated for otherembodiments and for reasons of comparison:

Curve 30: This is the case discussed with the weak-focusing arrangementand the telescope 18 associated to the long resonator arm 17. The pointof intersection of the curve 30 with the zero line is at R=4000 mm. Forthe practical embodiment in question (FIG. 12) precisely this mirror wasnot obtainable at short notice; therefore, an arrangement with a mirror26 with R=5000 mm was realized, cf. also the following explanationsregarding FIG. 12.

Curve 31: A telescope 18 in the long resonator arm 17 and a small radiusof curvature (such as, e.g., R=858 mm) would generate this curve 31. Therelations at R=858 mm (point 34) would yield a much poorer stability ascompared to curve 30. Even though there also exists a stable point(point 35) at which the changes are small, the former would be locatedat very large distances between the two mirrors (L=6 m).

Curve 32: If the weakly focusing telescope 18 (e.g. with a mirror radiusR=5000 mm) is associated to the short arm 16 of the original oscillator12, this curve 32 is formed. Here, again, the maximum of the stabilityis found at very small values of the distance L (<20 cm). Bythis—contrary to what is intended—no great overall lengthening of thelaser beam path would result.

Curve 33: In a combination of the short resonator arm 16 as telescopearm and a highly focusing arrangement, the maximum of the stability is,in fact, also at a very good location (at L=0.8 m), yet in this case atthat location the curve 33 has a great slope.

In practice, however, deviations in the production (of up to 10%) mayvery well occur in the mirror radii. Also, the model used is not quiteprecise, and deviations in the measured and calculated beam profile mayoccur. Therefore, it is even more important to find broad maximums (asin curve 30), and not critical ones (as in curve 33).

In FIGS. 11 to 15 curves relating to the transverse beam radius R′ in mmbelonging to actual embodiments are shown versus the resonator length xin m spread on a line (x-axis), these embodiments being based oncomputer simulations, the embodiment according to FIG. 12, however,having been realized in practice for test purposes.

In all the diagrams of FIGS. 11 to 15, the continuous line shows therelation at the ideal oscillator, in which all the length valuescorrespond to the theoretical values. The broken line simulates a (assuch very pronounced) deviation of 2 cm between the two telescopemirrors 25, 26. Is appears that in practice no large deviations occur,yet tests have shown that vibrations and temperature drifts occur. If,however, the laser (in the region of the short resonator arm 16)exhibits no drastic shifts even in case of large deviations it can beassumed that also slight vibrations which will lead to slight changes inthe distance, e.g. between the telescope mirrors 25, 26, will not playany role as regards the stability.

In FIG. 11, the beam radius R′ in transverse direction is indicated overthe resonator length x in m for a laser device 11, wherein the resonatordata are as follows:

-   -   short resonator arm 16: 65 cm;    -   long resonator arm 17: 120 cm (with the telescope 18 following        thereon);    -   distance between the telescope mirrors 25, 26: L/2=52 cm;    -   radius of the concave telescope mirror 26: R=3550 mm;    -   total length of oscillator 12: 10.22 m.

This diagram corresponds to an embodiment with an optimum in thestability of the resonator 12. However, here the distances between thetelescope mirrors 25, 26 are not very large so that the round trip timeof the laser pulses is not extended as much as desired and therepetition rate would merely be reduced to 14.6 MHz.

As has already been mentioned before, a concave mirror having a radiusR=5000 mm was available for practical investigations. With this mirroras telescope mirror 26, a laser device was built up as described, and itwas put up with the fact that the optimum stability (cf. the zero linein FIG. 10) is no longer given, but a slight deviation thereof, cf. thedot in the box on the curve 30 in FIG. 10. The deviations resulting inthis case are, however, tolerable, since the curve 30 in this region, ascan be seen from FIG. 10, is very flat, with a rise of practically =0.In FIG. 12, the associated diagram beam radius/resonator length isillustrated.

Here, the resonator data were as follows:

-   -   short resonator arm 16: 65 cm;    -   long resonator arm 17: 120 cm (telescope 18 following thereon);    -   distance between the telescope mirrors 25, 26: L/2 73.2 cm;    -   radius of the telescope mirror 26: R=5000 mm;    -   total length of the resonator 12: 13.6 m.

In FIG. 13, a case is illustrated in which a highly focusing arrangementin telescope 18 following the long resonator arm 17 is provided; thisresults in a not very stable configuration with regard to the variationof the mirrors 25, 26 of the telescope 18. This can be directlyrecognized from the diagram of FIG. 13 on the basis of the deviations ofthe broken line from the full line.

Resonator data:

-   -   short resonator arm 16: 65 cm;    -   long resonator arm 17: 120 cm (telescope 18 following thereon);    -   distance between the telescope mirrors 25, 26: L/2=73.2 cm;    -   radius of the telescope mirror 26: R=849 mm;    -   total length of resonator 12: 13.6 m.

Thus, the diagram according to FIG. 13 would approximately correspond tospot 34 on curve 31 in FIG. 10.

In FIG. 14 the case is illustrated in which the telescope 18 is arrangedto follow the short resonator arm 16, it being visible in comparison toFIG. 13 in case of a highly focusing arrangement in the telescope (aspreviously mentioned) that in terms of stability even somewhat betterconditions can be attained. This highly focusing arrangement is betteradapted to the short resonator arm 16. This is also shown by the beamdiameters which do not vary so much in FIG. 14 as compared to FIG. 13.

The resonator data regarding FIG. 14 are as follows:

-   -   short resonator arm 16: 65 cm (telescope 18 following thereon);    -   long resonator arm 17: 120 cm;    -   distance between the telescope mirrors 25, 26: L/2=73.2 cm;    -   radius of the telescope mirror 26: R=849 mm;    -   total length of resonator 12: 13.6 m.

Finally, from the diagram of FIG. 15 it appears how advantageous thecoupling of the telescope 18 into the long resonator arm 17 is, becauseif the telescope 18 is located to follow the short resonator arm 16, ahighly divergent laser beam 15 is in-coupled into the telescope 18. Incontrast to the representation given in FIG. 11, the first reflectionpoint of the weakly focusing telescope 18 therefore does not have theeffect of bundling the laser beam again. It is only the secondreflection point which achieves this collimation after a long path.Therefore, the maximum beam radius R′ on individual reflection points ofthe telescope mirror is >2 mm, i.e. the beam diameter is larger than 4mm. In practice, however, a space larger by the factor 3 must be presentat the telescope mirror for the respective beam in order not to lose anypower output. Here, however, this means that an area having a diameterof more than 1 cm must be present on the mirror per reflection point,whereby all the faults in the uniformity of the mirror will be found inthe laser beam images in magnified form, resulting in beam deformations.

The resonator data pertaining to FIG. 15 are as follows:

-   -   short resonator arm 16: 65 cm (telescope following thereon);    -   long resonator arm 17: 120 cm;    -   distance between the telescope mirrors 25, 26: L/2=73.2 cm;    -   radius of the concave telescope mirror 26: R 5000 mm;    -   total length of resonator 12: 13.6 m.

1. A short pulse laser device (11) with mode-locking, with a resonator(12) containing a laser crystal (14) as well as several mirrors (M1-M7,OC) which define a long resonator arm (17) as well as a short resonatorarm (16), one of which (M1) forms a pump beam in-coupling mirror, andanother one (OC) forms a laser beam out-coupler, and with a multiplereflection telescope (18) increasing the resonator length and associatedto one of the resonator arms (16, 17), which telescope is constructedusing mirrors (25, 26) in order to reflect a laser beam (15) coupledinto the space between them back and forth between the mirrors severaltimes before it is out-coupled back into the remaining resonator,sequential eccentric reflection points (1 to 8; 1′ to 8′) on the mirrors(25, 26) being offset relative to one another, characterized in that thetelescope (18) has only one curved mirror (26) as well as a plane mirror(25) whose position at least substantially corresponds to the middle(25′) of an imaginary multiple reflection arrangement with two curvedmirrors (26 a, 26 b), whereby the one curved mirror (26) of thetelescope (18) also contains the reflection points of the imaginaryother curved mirror.
 2. A short pulse laser device according to claim 1,characterized in that the curved mirror (26) is a concave mirror.
 3. Ashort-pulse laser device according to claim 1, characterized in that onthe one curved mirror (26), alternately reflection points of this mirroras well as reflection points of the imaginary other curved mirror arearranged on an imaginary circle line at arcuate distances correspondingto each other.
 4. A short-pulse laser device according to claim 1,characterized in that a total of eight reflection points (1 to 8) areprovided on the one curved mirror (26).
 5. A short-pulse laser deviceaccording to claim 1, characterized in that the distance between themirrors (25, 26) and the radius of curvature of the curved, concavemirror (26) correspond to the relation L/R=1±{square root}{overscore((1+cos α)/2)}, wherein L is twice the distance between the curvedmirror (26) and the plane mirror, R is the radius of curvature of thecurved mirror (26), and α is the central angle between two respectivesequential reflection points actually associated to the one curvedmirror and located on a circle line.
 6. A short-pulse laser deviceaccording to claim 5, characterized in that the curved mirror (26) ofthe telescope (18) is a concave mirror, for which it holds:L/R=1−{square root}{overscore ((1+cos α)/2)}
 7. A short-pulse laserdevice according to claim 1, characterized in that substantially in themiddle between the curved mirror (26) and the plane mirror (25), in- andout-coupling mirrors (24, 27) for the laser beam (15) are provided inthe path of one of the beam paths between these two mirrors.
 8. Ashort-pulse laser device according to claim 1, characterized in that thetelescope (18) is associated with the long resonator arm (17).
 9. Ashort-pulse laser device according to claim 1, characterized in that apassive mode-locking is provided as said mode-locking.
 10. A multiplereflection telescope (18) for a short-pulse laser device (11) forincreasing its resonator length, which telescope (18) is constructedusing mirrors (25, 26) so as to reflect a laser beam (15) coupled intothe space between them back and forth between the mirrors several timesbefore it is out-coupled back into the remaining laser device,sequential eccentric reflection points (1 to 8; 1′ to 8′) on the mirrors(25, 26) being offset relative to each other, characterized in that assaid telescope mirrors, only one curved mirror (26) as well as a planemirror (25) are provided, the position of the plane mirror (25) at leastsubstantially corresponding to the middle (25′) of an imaginary multiplereflection arrangement with two curved mirrors (26 a, 26 b), whereby theone curved mirror (26) of the telescope (18) also contains thereflection points of the imaginary other curved mirror.
 11. Amultiple-reflection telescope according to claim 10, characterized inthat the curved mirror (26) is a concave mirror.
 12. A telescopeaccording to claim 10, characterized in that on the one curved mirror(26) alternatingly reflection points of this mirror as well asreflection points of the imaginary other curved mirror are arranged onan imaginary circle line at arcuate distances corresponding to eachother.
 13. A telescope according to claim 10, characterized in that atotal of eight reflection points (1 to 8) are provided on the one curvedmirror (26).
 14. A telescope according to claim 10, characterized inthat the distance between the mirrors (25, 26) and the radius ofcurvature of the curved, concave mirror (26) correspond to the relationL/R=1±{square root}{overscore (1+cos α)/2)}, wherein L is twice thedistance between the curved mirror (26) and the plane mirror, R is theradius of curvature of the curved mirror (26), and α a is the centralangle between two respective sequential reflection points actuallyassociated to the one curved mirror and located on a circle line.
 15. Atelescope according to claim 14, characterized in that the curved mirror(26) of the telescope (18) is a concave mirror for which it holds:L/R=1−{square root}{overscore ((1+cos α)/2)}.
 16. A telescope accordingto claim 13, characterized in that substantially in the middle betweenthe curved mirror (26) and the plane mirror (25), in- and out-couplingmirrors (24, 27) for the laser beam (15) are provided in the path of oneof the beam paths between these two mirrors.